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1. Solve the pde 02и 2²u ay² T. az² дуг 1, on the inside of the equilateral triangle made up of the three sides y = √√3z- 2h/3, y = -√√3z2h/3 and y = h/3, subject to the boundary condition u = 0 on the actual triangle.

1. Solve the pde 02и 2²u ay² T. az² дуг 1, on the inside of the equilateral triangle made up of the three sides y = √√3z- 2h/3, y = -√√3z2h/3 and y = h/3, subject to the boundary condition u = 0 on the actual triangle.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the problem of steady flow through a circular cylinder of radius a and length L. Suppose the flow is driven by a pressure difference po- P1 over the distance L. In Cartesian coordinates, you can show that the velocity component down the axis of the cylinder is given by (po – P1) (a² – y² –²), 4µL и (у, 2) — 1. Solve the pde a²u , a?u = 1, dy2 ". əz² V3z – on the inside of the equilateral triangle made up of the three sides y = 2h/3, y = -V3z – 2h/3 and y = h/3, subject to the boundary condition u = 0 on the actual triangle.
Transcribed Image Text:Consider the problem of steady flow through a circular cylinder of radius a and length L. Suppose the flow is driven by a pressure difference po- P1 over the distance L. In Cartesian coordinates, you can show that the velocity component down the axis of the cylinder is given by (po – P1) (a² – y² –²), 4µL и (у, 2) — 1. Solve the pde a²u , a?u = 1, dy2 ". əz² V3z – on the inside of the equilateral triangle made up of the three sides y = 2h/3, y = -V3z – 2h/3 and y = h/3, subject to the boundary condition u = 0 on the actual triangle.
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